2A Symmetry Flashcards
An operation performed on an object which leaves it in a configuration that is indistinguishable from and superimposable on the original configuration
Symmetry operation
A symmetry operation is carried out with respect to
Points or lines or planes
Operation or element: rotate by 360/n
Operation
Operation or element: n fold axis
Element
Operation or element: reflection
Operation
Operation or element: mirror plane
Element
Operation or element: inversion through a center
Operation
Operation or element: point
Element
Operation or element: improper rotation
Operation
Operation or element: n fold axis and a mirror plane
Element
Molecule notation by
Schoenflies
Crystal notation by
Hermann-Mauguin
Symbol E
Identity
Symbol Cn
Rotation by 360/n; n fold symmetry axis
Symbol σ
Reflection, mirror plane
Symbol i
Inversion
Symbol Sn
Rotation followed by reflection in plane perpendicular to rotation axis; n fold axis of improper rotation
Properties of a group
Must have identity that commutes but leaves them unchanged (EA=AE=A). Must have inverse that yields the identity. Product of any two members must also be a member of the group. Associative property must hold A(BC)=(AB)C.
C1 symmetry
None other than identity operation
Cs symmetry
One mirror plane
Ci symmetry
Only inversion center